Cyclic modules of finite Gorenstein injective dimension and Gorenstein rings
Foxby, Hans-Bjørn ; Frankild, Anders J.
Illinois J. Math., Tome 51 (2007) no. 3, p. 67-82 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
The main result asserts that a local commutative Noetherian ring is Gorenstein, if it possesses a non-zero cyclic module of finite Gorenstein injective dimension. From this follows a classical result by Peskine and Szpiro stating that the ring is Gorenstein, if it admits a non-zero cyclic module of finite (classical) injective dimension. The main result applies to local homomorphisms of local rings and yields the next: if the source is a homomorphic image of a Gorenstein local ring and the target has finite Gorenstein injective dimension over the source, then the source is a Gorenstein ring. This, in turn, applies to the Frobenius endomorphism when the local ring is of prime equicharacteristic and is a homomorphic image of a Gorenstein local ring.
Publié le : 2007-01-15
Classification:  13D05,  13H10 
@article{1258735325,
     author = {Foxby, Hans-Bj\o rn and Frankild, Anders J.},
     title = {Cyclic modules of finite Gorenstein injective dimension and Gorenstein rings},
     journal = {Illinois J. Math.},
     volume = {51},
     number = {3},
     year = {2007},
     pages = { 67-82},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258735325}
}

Foxby, Hans-Bjørn; Frankild, Anders J. Cyclic modules of finite Gorenstein injective dimension and Gorenstein rings. Illinois J. Math., Tome 51 (2007) no. 3, pp.  67-82. http://gdmltest.u-ga.fr/item/1258735325/